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Full-adder is a digital circuit to perform arithmetic sum of two bits and a previous carry. It is represented in the diagram below. The circuit involves two half-adders & one OR gate. Alternately 2 XOR gates, 2 AND gates and 1 OR gate.
Click here for Verilog RTL example and test-bench for full-adder.
Truth table for Full-Adder (FA)
So the expressions for the full adder are:-
Sum_out = (in_x) XOR (in_y) XOR (carry_in)
Carry_out = (in_x) AND (in_y) OR (in_x xor in_y) and carry_in
Block Diagram of Full Adder